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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



On automorphisms of Danielewski surfaces

Author: Anthony J. Crachiola
Journal: J. Algebraic Geom. 15 (2006), 111-132
Published electronically: May 12, 2005
MathSciNet review: 2177197
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Abstract | References | Additional Information

Abstract: Let $\mathbf {k}$ be any field. Let $R = \mathbf {k}[X,Y,Z]/(X^n Y - Z^2 - h(X)Z)$, where $h(0) \ne 0$ and $n \geq 2$. We develop techniques for computing the AK invariant of a domain with arbitrary characteristic. We use these techniques to compute $\operatorname {AK}(R)$, describe the automorphism group of $R$, and describe the isomorphism classes of these algebras. We then show that these algebras provide counterexamples to the cancellation problem over any field, extending Danielewski’s original counterexample.

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Additional Information

Anthony J. Crachiola
Affiliation: Department of Mathematical Sciences, Saginaw Valley State University, 7400 Bay Road, University Center, Michigan 48710

Received by editor(s): November 15, 2004
Published electronically: May 12, 2005